Zilber-Pink for Hodge-generic curves in the Siegel modular threefold A_2

Claims the full curve case of Zilber-Pink in $\mathcal A_2$ over $\bar{\mathbb Q}$: a Hodge-generic algebraic curve contains only finitely many points whose abelian surface is isogenous to a product with a CM factor, to the square of a non-CM elliptic curve, or has quaternionic-division endomorphism algebra, besides finitely many special points. Previous unconditional results needed the curve to meet the Baily-Borel boundary or to have multiplicative degeneration. It does NOT treat higher-dimensional subvarieties of $\mathcal A_2$, $\mathcal A_g$ for $g\ge3$, or curves not defined over $\bar{\mathbb Q}$.

Claims the full curve case of Zilber-Pink in $\mathcal A_2$ over $\bar{\mathbb Q}$: a Hodge-generic algebraic curve contains only finitely many points whose abelian surface is isogenous to a product with a CM factor, to the square of a non-CM elliptic curve, or has quaternionic-division endomorphism algebra, besides finitely many special points. Previous unconditional results needed the curve to meet the Baily-Borel boundary or to have multiplicative degeneration. It does NOT treat higher-dimensional subvarieties of $\mathcal A_2$, $\mathcal A_g$ for $g\ge3$, or curves not defined over $\bar{\mathbb Q}$.